Subgroups — C₂²×C₃×#482 #10679109

Order 768.

2702 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#482	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#482	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₃×D₄	—	2	1	no	—
11	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
12	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×#121	—	2	6	no	—
16	C₂×C₃×#121	C₂²	1	12	yes	—
17	C₂×C₃×#117	—	2	6	no	—
18	C₂×C₃×#117	C₂²	1	12	yes	complemented
19	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₂²⋊C₄	—	2	1	no	—
23	C₂²×C₃×C₂²⋊C₄	—	2	1	no	—
24	C₂²×C₃×C₄²	—	2	1	no	—
25	C₃×#482	C₂²	1	64	yes	direct product factor
26	C₂×C₃×#107	C₂²	1	12	yes	complemented
27	C₂×C₃×#106	C₂²	1	12	yes	complemented
28	C₂×C₃×#102	C₂²	1	12	yes	complemented
29	C₂×C₃×#102	C₂²	1	12	yes	complemented
30	C₂×C₃×C₂²⋊C₈	C₂²	1	12	yes	complemented
31	C₂²×#121	C₂×C₃	1	1	yes	characteristic
32	C₂²×#117	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#482	C₂×C₃	1	24	yes	direct product factor
34	C₂²×#107	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂²×#106	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂²×#102	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂²×#102	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂⁵×C₃	—	2	1	no	—
40	C₂⁵×C₃	D₄	1	1	yes	characteristic
41	C₂²×C₃×D₄	—	2	12	no	—
42	C₂²×C₃×D₄	—	2	3	no	—
43	C₂²×C₃×D₄	—	2	4	no	—
44	C₂²×C₃×D₄	—	2	4	no	—
45	C₂²×C₃×D₄	—	4	8	no	—
46	C₂²×C₃×D₄	C₂³	1	6	yes	—
47	C₂³×C₃×C₄	—	2	4	no	—
48	C₂³×C₃×C₄	—	2	4	no	—
49	C₂³×C₃×C₄	—	2	1	no	—
50	C₂³×C₃×C₄	—	2	1	no	—
51	C₂³×C₃×C₄	—	2	1	no	—
52	C₂³×C₃×C₄	D₄	1	6	yes	—
53	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
54	C₂³×C₃×C₄	C₂³	1	6	yes	—
55	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₈	—	2	4	no	—
57	C₂²×C₃×C₈	—	2	4	no	—
58	C₂²×C₃×C₈	C₂³	1	6	yes	—
59	C₂²×C₃×C₈	C₂³	1	6	yes	—
60	C₃×#121	—	2	24	no	—
61	C₃×#121	C₂³	1	16	yes	—
62	C₃×#117	—	2	24	no	—
63	C₃×#117	C₂³	1	16	yes	complemented
64	C₂×C₃×C₄⋊C₄	—	2	3	no	—
65	C₂×C₃×C₄⋊C₄	—	2	3	no	—
66	C₂×C₃×C₄⋊C₄	—	2	3	no	—
67	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
68	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
69	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
70	C₂×C₃×C₂²⋊C₄	—	2	12	no	—
71	C₂×C₃×C₂²⋊C₄	—	2	12	no	—
72	C₂×C₃×C₄²	—	2	12	no	—
73	C₃×#107	C₂³	1	16	yes	complemented
74	C₃×#106	C₂³	1	16	yes	complemented
75	C₃×#102	C₂³	1	16	yes	complemented
76	C₃×#102	C₂³	1	16	yes	complemented
77	C₃×C₂²⋊C₈	C₂³	1	16	yes	complemented
78	C₂³×D₄	—	2	1	no	—
79	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
82	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
83	C₂×#121	—	2	6	no	—
84	C₂×#121	C₂²×C₃	1	12	yes	—
85	C₂×#117	—	2	6	no	—
86	C₂×#117	C₂²×C₃	1	12	yes	complemented
87	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₂²⋊C₄	—	2	1	no	—
91	C₂²×C₂²⋊C₄	—	2	1	no	—
92	C₂²×C₄²	—	2	1	no	—
93	#482	C₂²×C₃	1	64	yes	direct product factor
94	C₂×#107	C₂²×C₃	1	12	yes	complemented
95	C₂×#106	C₂²×C₃	1	12	yes	complemented
96	C₂×#102	C₂²×C₃	1	12	yes	complemented
97	C₂×#102	C₂²×C₃	1	12	yes	complemented
98	C₂×C₂²⋊C₈	C₂²×C₃	1	12	yes	complemented
99	C₂⁴×C₃	—	2	4	no	—
100	C₂⁴×C₃	—	2	4	no	—
101	C₂⁴×C₃	—	2	4	no	—
102	C₂⁴×C₃	—	2	6	no	—
103	C₂⁴×C₃	—	4	4	no	—
104	C₂⁴×C₃	—	4	4	no	—
105	C₂⁴×C₃	—	4	4	no	—
106	C₂⁴×C₃	C₂×D₄	1	6	yes	—
107	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×D₄	—	2	16	no	—
109	C₂×C₃×D₄	—	2	6	no	—
110	C₂×C₃×D₄	—	2	12	no	—
111	C₂×C₃×D₄	—	2	12	no	—
112	C₂×C₃×D₄	—	4	48	no	—
113	C₂×C₃×D₄	—	4	12	no	—
114	C₂×C₃×D₄	C₂⁴	1	4	yes	—
115	C₂²×C₃×C₄	—	2	4	no	—
116	C₂²×C₃×C₄	—	2	24	no	—
117	C₂²×C₃×C₄	—	2	12	no	—
118	C₂²×C₃×C₄	—	2	12	no	—
119	C₂²×C₃×C₄	—	2	6	no	—
120	C₂²×C₃×C₄	—	2	6	no	—
121	C₂²×C₃×C₄	—	2	6	no	—
122	C₂²×C₃×C₄	—	4	4	no	—
123	C₂²×C₃×C₄	—	4	4	no	—
124	C₂²×C₃×C₄	—	4	4	no	—
125	C₂²×C₃×C₄	C₂×D₄	1	6	yes	—
126	C₂²×C₃×C₄	C₂×D₄	1	12	yes	—
127	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
128	C₂²×C₃×C₄	#41	1	4	yes	—
129	C₂²×C₃×C₄	#41	1	4	yes	—
130	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
131	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
132	C₂×C₃×C₈	—	2	12	no	—
133	C₂×C₃×C₈	—	2	12	no	—
134	C₂×C₃×C₈	C₂⁴	1	4	yes	—
135	C₂×C₃×C₈	C₂⁴	1	4	yes	—
136	C₃×C₄⋊C₄	—	2	6	no	—
137	C₃×C₄⋊C₄	—	2	6	no	—
138	C₃×C₄⋊C₄	—	2	6	no	—
139	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
140	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
141	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
142	C₃×C₂²⋊C₄	—	2	16	no	—
143	C₃×C₂²⋊C₄	—	2	16	no	—
144	C₃×C₄²	—	2	16	no	—
145	C₂⁵	—	2	1	no	—
146	C₂⁵	C₃×D₄	1	1	yes	characteristic
147	C₂²×D₄	—	2	12	no	—
148	C₂²×D₄	—	2	3	no	—
149	C₂²×D₄	—	2	4	no	—
150	C₂²×D₄	—	2	4	no	—
151	C₂²×D₄	—	4	8	no	—
152	C₂²×D₄	C₂³×C₃	1	6	yes	—
153	C₂³×C₄	—	2	4	no	—
154	C₂³×C₄	—	2	4	no	—
155	C₂³×C₄	—	2	1	no	—
156	C₂³×C₄	—	2	1	no	—
157	C₂³×C₄	—	2	1	no	—
158	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
159	C₂³×C₄	C₃×D₄	1	6	yes	—
160	C₂³×C₄	C₂³×C₃	1	6	yes	—
161	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₈	—	2	4	no	—
163	C₂²×C₈	—	2	4	no	—
164	C₂²×C₈	C₂³×C₃	1	6	yes	—
165	C₂²×C₈	C₂³×C₃	1	6	yes	—
166	#121	—	2	24	no	—
167	#121	C₂³×C₃	1	16	yes	—
168	#117	—	2	24	no	—
169	#117	C₂³×C₃	1	16	yes	complemented
170	C₂×C₄⋊C₄	—	2	3	no	—
171	C₂×C₄⋊C₄	—	2	3	no	—
172	C₂×C₄⋊C₄	—	2	3	no	—
173	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
174	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
175	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
176	C₂×C₂²⋊C₄	—	2	12	no	—
177	C₂×C₂²⋊C₄	—	2	12	no	—
178	C₂×C₄²	—	2	12	no	—
179	#107	C₂³×C₃	1	16	yes	complemented
180	#106	C₂³×C₃	1	16	yes	complemented
181	#102	C₂³×C₃	1	16	yes	complemented
182	#102	C₂³×C₃	1	16	yes	complemented
183	C₂²⋊C₈	C₂³×C₃	1	16	yes	complemented
184	C₂³×C₃	—	2	12	no	—
185	C₂³×C₃	—	2	12	no	—
186	C₂³×C₃	—	2	12	no	—
187	C₂³×C₃	—	2	4	no	—
188	C₂³×C₃	—	4	16	no	—
189	C₂³×C₃	—	4	12	no	—
190	C₂³×C₃	—	4	12	no	—
191	C₂³×C₃	—	4	12	no	—
192	C₂³×C₃	—	8	16	no	—
193	C₂³×C₃	#123	1	4	yes	—
194	C₂³×C₃	#135	1	4	yes	—
195	C₂³×C₃	AGL(1,ℤ/8)	1	4	yes	—
196	C₂³×C₃	C₂²×D₄	1	4	yes	—
197	C₂³×C₃	C₂²×D₄	1	3	yes	—
198	C₃×D₄	—	2	4	no	—
199	C₃×D₄	—	2	4	no	—
200	C₃×D₄	—	4	32	no	—
201	C₃×D₄	—	4	12	no	—
202	C₂×C₃×C₄	—	2	12	no	—
203	C₂×C₃×C₄	—	2	24	no	—
204	C₂×C₃×C₄	—	2	4	no	—
205	C₂×C₃×C₄	—	2	4	no	—
206	C₂×C₃×C₄	—	2	4	no	—
207	C₂×C₃×C₄	—	2	4	no	—
208	C₂×C₃×C₄	—	2	4	no	—
209	C₂×C₃×C₄	—	4	12	no	—
210	C₂×C₃×C₄	—	4	12	no	—
211	C₂×C₃×C₄	—	4	12	no	—
212	C₂×C₃×C₄	#123	1	12	yes	—
213	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
214	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
215	C₂×C₃×C₄	C₂×#41	1	6	yes	—
216	C₂×C₃×C₄	C₂×#41	1	6	yes	—
217	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
218	C₃×C₈	—	2	4	no	—
219	C₃×C₈	—	2	4	no	—
220	C₂⁴	—	2	4	no	—
221	C₂⁴	—	2	4	no	—
222	C₂⁴	—	2	4	no	—
223	C₂⁴	—	2	6	no	—
224	C₂⁴	—	4	4	no	—
225	C₂⁴	—	4	4	no	—
226	C₂⁴	—	4	4	no	—
227	C₂⁴	C₂×C₃×D₄	1	6	yes	—
228	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
229	C₂×D₄	—	2	16	no	—
230	C₂×D₄	—	2	6	no	—
231	C₂×D₄	—	2	12	no	—
232	C₂×D₄	—	2	12	no	—
233	C₂×D₄	—	4	48	no	—
234	C₂×D₄	—	4	12	no	—
235	C₂×D₄	C₂⁴×C₃	1	4	yes	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	24	no	—
238	C₂²×C₄	—	2	12	no	—
239	C₂²×C₄	—	2	12	no	—
240	C₂²×C₄	—	2	6	no	—
241	C₂²×C₄	—	2	6	no	—
242	C₂²×C₄	—	2	6	no	—
243	C₂²×C₄	—	4	4	no	—
244	C₂²×C₄	—	4	4	no	—
245	C₂²×C₄	—	4	4	no	—
246	C₂²×C₄	C₂×C₃×D₄	1	6	yes	—
247	C₂²×C₄	C₂×C₃×D₄	1	12	yes	—
248	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
249	C₂²×C₄	C₃×#41	1	4	yes	—
250	C₂²×C₄	C₃×#41	1	4	yes	—
251	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
252	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
253	C₂×C₈	—	2	12	no	—
254	C₂×C₈	—	2	12	no	—
255	C₂×C₈	C₂⁴×C₃	1	4	yes	—
256	C₂×C₈	C₂⁴×C₃	1	4	yes	—
257	C₄⋊C₄	—	2	6	no	—
258	C₄⋊C₄	—	2	6	no	—
259	C₄⋊C₄	—	2	6	no	—
260	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
261	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
262	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
263	C₂²⋊C₄	—	2	16	no	—
264	C₂²⋊C₄	—	2	16	no	—
265	C₄²	—	2	16	no	—
266	C₂²×C₃	—	2	4	no	—
267	C₂²×C₃	—	2	4	no	—
268	C₂²×C₃	—	2	4	no	—
269	C₂²×C₃	—	4	24	no	—
270	C₂²×C₃	—	4	4	no	—
271	C₂²×C₃	—	4	4	no	—
272	C₂²×C₃	—	4	4	no	—
273	C₂²×C₃	—	8	24	no	—
274	C₂²×C₃	#482	1	16	yes	direct product factor
275	C₂²×C₃	C₂×#123	1	6	yes	—
276	C₂²×C₃	C₂×#135	1	6	yes	—
277	C₂²×C₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
278	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
279	C₃×C₄	—	2	4	no	—
280	C₃×C₄	—	4	4	no	—
281	C₃×C₄	—	4	4	no	—
282	C₃×C₄	—	4	4	no	—
283	C₃×C₄	C₂×#123	1	6	yes	—
284	C₃×C₄	C₂²×#41	1	1	yes	characteristic
285	C₃×C₄	C₂²×#41	1	1	yes	characteristic
286	C₂³	—	2	12	no	—
287	C₂³	—	2	12	no	—
288	C₂³	—	2	12	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	4	16	no	—
291	C₂³	—	4	12	no	—
292	C₂³	—	4	12	no	—
293	C₂³	—	4	12	no	—
294	C₂³	—	8	16	no	—
295	C₂³	C₃×#123	1	4	yes	—
296	C₂³	C₃×#135	1	4	yes	—
297	C₂³	C₃×AGL(1,ℤ/8)	1	4	yes	—
298	C₂³	C₂²×C₃×D₄	1	4	yes	—
299	C₂³	C₂²×C₃×D₄	1	3	yes	—
300	D₄	—	2	4	no	—
301	D₄	—	2	4	no	—
302	D₄	—	4	32	no	—
303	D₄	—	4	12	no	—
304	C₂×C₄	—	2	12	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	24	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	4	12	no	—
312	C₂×C₄	—	4	12	no	—
313	C₂×C₄	—	4	12	no	—
314	C₂×C₄	C₃×#123	1	12	yes	—
315	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
316	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
317	C₂×C₄	C₂×C₃×#41	1	6	yes	—
318	C₂×C₄	C₂×C₃×#41	1	6	yes	—
319	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
320	C₈	—	2	4	no	—
321	C₈	—	2	4	no	—
322	C₂×C₃	—	4	4	no	—
323	C₂×C₃	—	8	4	no	—
324	C₂×C₃	C₂×#482	1	12	yes	direct product factor
325	C₂×C₃	C₂²×#123	1	1	yes	characteristic
326	C₂×C₃	C₂²×#135	1	1	yes	characteristic
327	C₂×C₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
328	C₂²	—	2	4	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	4	24	no	—
332	C₂²	—	4	4	no	—
333	C₂²	—	4	4	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	8	24	no	—
336	C₂²	C₃×#482	1	16	yes	direct product factor
337	C₂²	C₂×C₃×#123	1	6	yes	—
338	C₂²	C₂×C₃×#135	1	6	yes	—
339	C₂²	C₂×C₃×AGL(1,ℤ/8)	1	6	yes	—
340	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
341	C₄	—	2	4	no	—
342	C₄	—	4	4	no	—
343	C₄	—	4	4	no	—
344	C₄	—	4	4	no	—
345	C₄	C₂×C₃×#123	1	6	yes	—
346	C₄	C₂²×C₃×#41	1	1	yes	characteristic
347	C₄	C₂²×C₃×#41	1	1	yes	characteristic
348	C₃	C₂²×#482	1	1	yes	characteristic, direct product factor, Sylow
349	C₂	—	4	4	no	—
350	C₂	—	8	4	no	—
351	C₂	C₂×C₃×#482	1	12	yes	direct product factor
352	C₂	C₂²×C₃×#123	1	1	yes	characteristic
353	C₂	C₂²×C₃×#135	1	1	yes	characteristic
354	C₂	C₂²×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂²×C₃×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂⁴×C₃×C₄ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂²×C₃×#117	C₂	semidirect
3. C₂×C₃×#482	C₂	direct (N × H)
4. C₂²×C₃×#107	C₂	semidirect
5. C₂²×C₃×#106	C₂	semidirect
6. C₂²×C₃×#102	C₂	semidirect
7. C₂²×C₃×#102	C₂	semidirect
8. C₂²×C₃×C₂²⋊C₈	C₂	semidirect
9. C₂²×#482	C₃	direct (N × H)
18. C₂×C₃×#117	C₂²	semidirect
25. C₃×#482	C₂²	direct (N × H)
26. C₂×C₃×#107	C₂²	semidirect
27. C₂×C₃×#106	C₂²	semidirect
28. C₂×C₃×#102	C₂²	semidirect
29. C₂×C₃×#102	C₂²	semidirect
30. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
32. C₂²×#117	C₂×C₃	semidirect
33. C₂×#482	C₂×C₃	direct (N × H)
34. C₂²×#107	C₂×C₃	semidirect
35. C₂²×#106	C₂×C₃	semidirect
36. C₂²×#102	C₂×C₃	semidirect
37. C₂²×#102	C₂×C₃	semidirect
38. C₂²×C₂²⋊C₈	C₂×C₃	semidirect
63. C₃×#117	C₂³	semidirect
73. C₃×#107	C₂³	semidirect
74. C₃×#106	C₂³	semidirect
75. C₃×#102	C₂³	semidirect
76. C₃×#102	C₂³	semidirect
77. C₃×C₂²⋊C₈	C₂³	semidirect
86. C₂×#117	C₂²×C₃	semidirect
93. #482	C₂²×C₃	direct (N × H)
94. C₂×#107	C₂²×C₃	semidirect
95. C₂×#106	C₂²×C₃	semidirect
96. C₂×#102	C₂²×C₃	semidirect
97. C₂×#102	C₂²×C₃	semidirect
98. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
169. #117	C₂³×C₃	semidirect
179. #107	C₂³×C₃	semidirect
180. #106	C₂³×C₃	semidirect
181. #102	C₂³×C₃	semidirect
182. #102	C₂³×C₃	semidirect
183. C₂²⋊C₈	C₂³×C₃	semidirect
274. C₂²×C₃	#482	direct (N × H)
324. C₂×C₃	C₂×#482	direct (N × H)
336. C₂²	C₃×#482	direct (N × H)
348. C₃	C₂²×#482	direct (N × H)
351. C₂	C₂×C₃×#482	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×#121	2
C₂²×C₃×#117	2
C₂×C₃×#482	2
C₂²×C₃×#107	2
C₂²×C₃×#106	2
C₂²×C₃×#102	2
C₂²×C₃×C₂²⋊C₈	2
C₂²×#482	3

Subgroups — C22×C3×#482 #10679109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#482 #10679109